Addition reaction of adamantylideneadamantane with Br2 and 2Br2: a computational study

Ab initio calculations were carried out for the reaction of adamantylideneadamantane (Ad=Ad) with Br2 and 2Br2. Geometries of the reactants, transition states, intermediates, and products were optimized at HF and B3LYP levels of theory using the 6-31G(d) basis set. Energies were also obtained using single point calculations at the MP2/6-31G(d)//HF/6-31G(d), MP2/6-31G(d)//B3LYP/6-31G(d), and B3LYP/6-31+G(d)//B3LYP/6-31G(d) levels of theory. Intrinsic reaction coordinate (IRC) calculations were performed to characterize the transition states on the potential energy surface. Only one pathway was found for the reaction of Ad=Ad with one Br2 producing a bromonium/bromide ion pair. Three mechanisms for the reaction of Ad=Ad with 2Br2 were found, leading to three different structural forms of the bromonium/Br3- ion pair. Activation energies, free energies, and enthalpies of activation along with the relative stability of products for each reaction pathway were calculated. The reaction of Ad=Ad with 2Br2 was strongly favored over the reaction with only one Br2. According to B3LYP/6-31G(d) and single point calculations at MP2, the most stable bromonium/Br3- ion pair would form spontaneously. The most stable of the three bromonium/Br3- ion pairs has a structure very similar to the observed X-ray structure. Free energies of activation and relative stabilities of reactants and products in CCl4 and CH2ClCH2Cl were also calculated with PCM using the united atom (UA0) cavity model and, in general, results similar to the gas phase were obtained. An optimized structure for the trans-1,2-dibromo product was also found at all levels of theory both in gas phase and in solution, but no transition state leading to the trans-1,2-dibromo product was obtained.     

Water-trapping of unstable carbocations taking place into the inverted region of the Marcus equation. First experimental and computational evidence

The reaction rates of the water-trapping of unstable 1-norbornyl cations in relation to the rates of their rearrangement (ring contraction) have been experimentally determined. The activation barrier of the rearrangement reactions was calculated with the QST2 method, whereas the Marcus theory was applied to predict the activation barrier of the trapping reaction. All computations in gas phase were performed with the DFT B3LYP/6-31G(d) method, while the PCM model was used for the computation of unspecific solvent effects. The established methodology was able to predict the major product formed in the solvolysis of the corresponding triflate precursors of the studied carbocations. The agreement between experiment and theory supports, for the first time, the interesting conclusion that the very exergonic trapping-reaction of unstable 1-norbornyl cations takes place with relatively high barriers of activation and, hence, into the Marcus inverted region. Additionally, a noteworthy relationship between the free energy of activation for the carbocation rearrangement in gas phase and the length of the rearranging bond in the ground state is reported.     

Theoretical studies on the effects of methods and parameterization on the calculated free energy of hydration for small molecules

Free energies of hydration (FEH) have been computed for 13 neutral and nine ionic species as a difference of theoretically calculated Gibbs free energies in solution and in the gas phase. In‐solution calculations have been performed using both SCIPCM and PCM polarizable continuum models at the density functional theory (DFT)/B3LYP and ab initio Hartree–Fock levels with two basis sets (6‐31G* and 6‐311++G**). Good linear correlation has been obtained for calculated and experimental gas‐phase dipole moments, with an increase by ～30% upon solvation due to solute polarization. The geometry distortion in solution turns out to be small, whereas solute polarization energies are up to 3 kcal/mol for neutral molecules. Calculation of free energies of hydration with PCM provides a balanced set of values with 6‐31G* and 6‐311++G** basis sets for neutral molecules and ionic species, respectively. Explicit solvent calculations within Monte Carlo simulations applying free energy perturbation methods have been considered for 12 neutral molecules. Four different partial atomic charge sets have been studied, obtained by a fit to the gas‐phase and in‐solution molecular electrostatic potentials at in‐solution optimized geometries. Calculated FEH values depend on the charge set and the atom model used. Results indicate a preference for the all‐atom model and partial charges obtained by a fit to the molecular electrostatic potential of the solute computed at the SCIPCM/B3LYP/6‐31G* level. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Cyclic vinyl p-tolyl sulfilimines as chiral dienophiles: theoretical study on the stereoselectivity, Lewis acid catalysis, and solvent effects in their Diels-Alder reactions

The theoretical study reported in the present work deals with chiral cyclic vinyl sulfilimines and their reactivity as dienophiles in [4 + 2] cycloaddition reactions, using B3LYP/6-31G(d)//AM1 and B3LYP/6-31G(d)//B3LYP/6-31G(d) model chemistries. Consideration of Lewis acid catalysis, illustrated by BF(3), decreases the activation energies of the cycloaddition process while the charge transfer from the diene to the sulfilimine is augmented. The [4 + 2] cycloaddition reactions of sulfilimines with both furan and cyclopentadiene occur in the gas phase with endo stereoselectivity, which is more pronounced with the latter diene. Endo-exo energy differences in the gas phase with the B3LYP/6-31+G(d)//B3LYP/6-31+G(d), B3LYP/6-31G(d)//B3LYP/6-31G(d), and B3LYP/6-31G(d)//AM1 model chemistries are almost the same. Solvent effects are responsible for the inversion of the stereoselectivity in the reactions of sulfilimines with furan because of the great difference in the dipole moments in endo and exo approaches.     

HO3、HO+3、HO-3光谱和结构的MP2和DFT理论研究

用B3LYP和MP2量子化学理论,详细地计算了HO3、HO+3、HO-3可能的平衡构型、能量和光谱参数,分析了它们可能的解离通道和稳定性.还分析了HO3的电离势(IE)及电子亲和势(Ea),讨论了HO3、HO3-自由基的光电子能谱的特征,及用光电子能谱去探测HO3的可能性.     

Attachment of Chloride Anion to Sugars: Mechanistic Investigation and Discovery of a New Dopant for Efficient Sugar Ionization/Detection in Mass Spectrometers

A new method for efficient ionization of sugars in the negative‐ion mode of electrospray mass spectrometry is presented. Instead of using strongly hydrophobic dopants such as dichloromethane or chloroform, efficient ionization of sugars has been achieved by using aqueous HCl solution for the first time. This methodology makes it possible to use hydrophilic dopants, which are more appropriate for chromatographic separation techniques with efficient sugar ionization and detection in mass spectrometry. The interaction between chloride anions and monosaccharides (glucose and galactose) was studied by DFT in the gas phase and by implementing the polarizable continuum model (PCM) for calculations in solution at the high B3LYP/6‐31+G(d,p)//B3LYP/6‐311+G(2d,p) level of theory. In all optimized geometries of identified [M+Cl]^? anions, a non‐covalent interaction exists. Differences were revealed between monodentate and bidentate complex anions, with the latter having noticeably higher binding energies. The calculated affinity of glucose and galactose toward the chloride anion in the gas phase and their chloride anion binding energies in solution are in excellent agreement with glucose and galactose [M+Cl]^? experimental intensity profiles that are represented as a function of the chloride ion concentration. Density functional calculations of gas‐phase affinities toward chloride anion were also performed for the studied disaccharides sucrose and gentiobiose. All calculations are in excellent agreement with the experimental data. An example is introduced wherein HCl was used to effectively ionize sugars and form chlorinated adduct anions to detect sugars and glycosylated metabolites (anthocyanins) in real biological systems (Vitis vinifera grape extracts and wines), whereas they would not have been easily detectable under standard infusion electrospray mass spectrometry conditions as deprotonated species.     

Mechanisms for the deamination reaction of cytosine with H2O/OH(-) and 2H2O/OH(-): a computational study

Mechanisms for the deamination reaction of cytosine with H 2O/OH (-) and 2H 2O/OH (-) to produce uracil were investigated using ab initio calculations. Optimized geometries of reactants, transition states, intermediates, and products were determined at MP2 and B3LYP using the 6-31G(d) basis set and at B3LYP/6-31+G(d) levels of theory. Single point energies were also determined at MP2/G3MP2Large and G3MP2 levels of theory. Thermodynamic properties (Delta E, Delta H, and Delta G), activation energies, enthalpies, and free energies of activation were calculated for each reaction pathway investigated. Intrinsic reaction coordinate (IRC) analysis was performed to characterize the transition states on the potential energy surface. Seven pathways for the deamination reaction were found. All pathways produce an initial tetrahedral intermediate followed by several conformational changes. The final intermediate for all pathways dissociates to product via a 1-3 proton shift. The activation energy for the rate-determining step, the formation of the tetrahedral intermediate for pathway D, the only pathway that can lead to uracil, is 115.3 kJ mol (-1) at the G3MP2 level of theory, in excellent agreement with the experimental value (117 +/- 4 kJ mol (-1)).     

Theoretical studies on the intramolecular hydrogen bond and tautomerism of 8-mercaptoquinoline in the gaseous phase and in solution using modern DFT methods

A theoretical quantum chemical study of the intramolecular hydrogen bonding interactions in 8-mercaptoquinoline has been carried out. Special attention has been paid to the rotation of S-H bond and intramolecular proton-transfer reactions. Therewith, the B3LYP/6-311++G(d,p), B3LYP/6-31+G(2d,2p), MPW1K/6-311++G(d,p), MPW1K/6-31+G(2d,2p), BH&HLYP/6-311++G(d,p), and G96LYP/6-311++G(d,p) methods have been used. By means of the Onsager and PCM reaction field methods, the effects of solvent on hydrogen-bond energies, conformational equilibria, rotational barriers, and tautomerism in aqueous solution have been studied. These simulations were done at the MPW1K/6-311++G(d,p) and B3LYP/6-311++G(d,p) levels. Natural-bond orbital analysis has been performed to study the intramolecular hydrogen bond (IHB) in the gaseous phase and in aqueous medium. The stability of forms under consideration in solution does not coincide with that in the gaseous phase, underlining a great importance of the electrostatic influence of solvent. Double-proton transfer in the prototropic tautomerization of 8-mercaptoquinoline, one water molecule complex in the gaseous phase and in solution, has been systematically studied. The double-proton transfer occurs concertedly and synchronously. The water-assisted tautomerization is kinetically less, but thermodynamically more favorable, compared to that of the single-proton transfer. As in the case with single-proton transfer, for water-assisted reaction, the tautomerization energies and barrier heights decrease with the increase in dielectric constant, which implies faster and more complete tautomerization of 8-mercaptoquinoline in a polar solvent.     

Ab initio study of 2,4-substituted azolidines. II. Amino-imino tautomerism of 2-aminothiazolidine-4-one and 4-aminothiazolidine-2-one in water solution

The relative stabilities of the tautomers of 2-aminothiazolidine-4-one and 4-aminothiazolidine-2-one were calculated at the MP2/6-31+G(d,p) level by considering their mono- and trihydrated complexes. Single-point calculations at the MP4/6-31+G(d,p)//MP2/6-31+G(d,p) level of theory were performed to obtain more accurate energies. The values of proton transfer barriers in the isolated, mono- and trihydrated tautomers of 2-aminothiazolidine-4-one (2AT) and 4-aminothiazolidine-2-one (4AT) were calculated for two different mechanisms of tautomerisation. In the absence of water, the process of proton transfer should not occur. Addition of water molecules decreases the barrier making the process faster, as the participation of two water molecules in a proton transfer reaction is more favorable than the participation of only one water molecule. To estimate the effect of the medium (water) on the relative stabilities of the tautomers of the studied compounds we applied the polarizable continuum model (PCM). (13)C NMR chemical shieldings were calculated using the GIAO approach at MP2/6-31+G(d,p) optimized geometries. HF and the DFT B3LYP functional with 6-31+G(d,p) basis set were employed. The quantum chemical results for the chemical shifts in gas phase and in polar solvents (water and DMSO) were compared with experimental data. TD DFT B3LYP/aug-cc-pVTZ calculations were performed to predict the absorption maxima of tautomers A and B of 2AT and 4AT.     

An ab initio and density functional theory study of keto-enol equilibria of hydroxycyclopropenone in gas and aqueous solution phase

Keto-enol tautomerism in hydroxycyclopropenone (2-hydroxy-2-cyclopropen-1-one) has been studied using ab initio methods, the B3LYP functional of density functional theory, as well as complete basis set (CBS-QB3 and CBS-APNO) and G3 methods. Absolute and relative energies were calculated with each of the methods, whereas computations of geometries and harmonic frequencies for hydroxycyclopropenone and 1,2-cyclopropanedione were computed in the gas phase but were limited to HF, MP2 and CCSD levels of theory, and the B3LYP functional, in combination with the 6-31++G** basis set. Using the MP2/6-31++G** gas phase optimized structure, each species was then optimized fully in aqueous solution by employing the polarizable continuum model (PCM) self-consistent reaction field approach, in which HF, MP2 and B3LYP levels of theory were utilized, with the same 6-31++G** basis set. In both gas and aqueous solution phases, the keto form is higher in energy for all of the model chemistries considered. The presence of the solvent, however, is found to have very little effect on the bond lengths, angles and harmonic frequencies. From the B3LYP/6-31++G** Gibbs free energy, the keto-enol tautomeric equilibrium constant for 2-hydroxy-2-cyclopropen-1-one <==> 1,2-cyclopropanedione is computed to be K(T)(gas) = 2.35 x 10(-6), K(T)(aq) = 5.61 x 10(-14). It is concluded that the enol form is overwhelmingly predominant in both environments, with the effect of the solvent shifting the direction of equilibrium even more strongly in the favor of hydroxycyclopropenone. The almost exclusive nature of this species is attributed to stabilization resulting from aromaticity. Confirmation is provided by comparison of the simulated vibrational spectra of hydroxycyclopropenone with the measured infrared spectrum in an argon matrix.     

Unusual solvent effect on a SN2 reaction. A quantum-mechanical and kinetic study of the Menshutkin reaction between 2-amino-1-methylbenzimidazole and iodomethane in the gas phase and in acetonitrile

The quaternization reaction between 2-amino-1-methylbenzimidazole and iodomethane was investigated in the gas phase and in liquid acetonitrile. Both experimental and theoretical techniques were used in this study. In the experimental part of this work, accurate second-order rate constants were obtained for this reaction in acetonitrile from conductivity data in the 293-323 K temperature range and at ambient pressure. From two different empirical equations describing the effect of temperature on reaction rates, thermodynamic functions of activation were calculated. In the theoretical part of this work, the mechanism of this reaction was investigated in the gas phase and in acetonitrile. Two different quantum levels (B3LYP/[6-311++G(3df,3pd)/LanL2DZ]//B3LYP/[6-31G(d)/LanL2DZ] and B3LYP/[6-311++G(3df,3pd)/LanL2DZ]//B3LYP/[6-31+G(d)/LanL2DZ]) were used in the calculations, and the acetonitrile environment was modeled using the polarized continuum model (PCM). In addition, an atoms in molecules (AIM) analysis was made aiming to characterize possible hydrogen bonding. The results obtained by both techniques are in excellent agreement and lead to new insight into the mechanism of the reaction under examination. These include the identification and thermodynamic characterization of the relevant stationary species, the rationalization of the mechanistic role played by the solvent and the amine group adjacent to the nucleophile nitrogen atom, the proposal of alternative paths on the modeled potential energy surfaces, and the origin of the marked non-Arrhenius behavior of the kinetic data in solvent acetonitrile. In particular, the AIM analysis confirmed the operation of intermolecular hydrogen bonds between reactants and between products, both in the gas phase and in solution. It is also concluded that the unusual solvent effect on this Menshutkin reaction stems from the conjunction of a nucleophile possessing a relatively complex chemical structure with a dipolar aprotic solvent that is protophobic.     

Imidoylketene-alpha-oxoketenimine and alpha-oxoketene-alpha-oxoketene rearrangements. 1,3-shifts of substituted phenyl groups

1,3-phenyl shifts interconvert imidoylketenes 1 and alpha-oxoketenimines 2 and, likewise, alpha-oxoketenes 3 automerize by this 1,3-shift. These rearrangements usually take place in the gas phase under conditions of flash vacuum thermolysis. Energy profiles calculated at the B3LYP/6-31G(d,p) and B3LYP/6311 + G(3df,2p)//B3LYP/6-31G(d,p) levels demonstrate that electron donating substituents (D) in the migrating phenyl group and electron withdrawing ones (W) in the non-migrating phenyl group, can stabilise the transition states TS1 and TS2 to the extent that activation barriers of ca. 100 kJ mol(-1) or less are obtained; i.e. enough to make these reactions potentially observable in solution at ordinary temperatures. The calculated transition state energies DeltaG(TS1) show an excellent correlation with the Hammett constants sigma(p)(W) and sigma(p+)(D).     

Theoretical calculation of the pKa values of some drugs in aqueous solution

In this work, calculations of pK_a values have been performed on benzoic acid and its para‐substituted derivatives and some drugs by using Gaussian 98 software package. Gas‐phase energies were calculated with HF/6‐31 G** and B3LYP/6‐31 G** levels of theory. Free energies of solvation have been computed using the polarizable continuum model (PCM), conductor‐like PCM (CPCM), and the integral equation formalism‐PCM at the same levels which have been used for geometry determination in the gas‐phase. The results that show the calculated pK_a values using the B3LYP are better than those using the corresponding HF. In comparison to the other models, the results obtained indicate that the PCM model is a suitable solvation model for calculating pK_a values. For the investigated compounds, a good agreement between the experimental and the calculated pK_a values was also observed. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

An exploration of conformational search of leucine molecule and their vibrational spectra in gas phase using ab initio methods

An extensive exploration of the conformational space has been carried out to characterize all possible gas phase structures of leucine. A total of 324 unique trial structures for canonical leucine were generated by considering all possible combinations of single bond rotamers. All trial structures were optimized at the B3LYP/6-311G* level of the DFT method. A total of 77 unique and stationary canonical conformers were found. Further, 15 most stable conformers were reoptimized at B3LYP/6-311++G** level and their respective relative energies, vertical ionization energies, hydrogen bonding patterns, rotational constants and dipole moments were calculated. A single point energy calculations for leucine conformers have also been done at both B3LYP/6-311++G(2df, p) and MP2/6-311++G(2df, p) levels. The good agreement between our estimates of rotational constants for two most stable conformers and available experimental measurements supports the reliability of the B3LYP/6-311++G** level of theory for describing the conformational behavior of leucine molecule. The proton affinity and gas phase basicity were also determined. Using the statistical approach, conformational distributions at various temperatures have also been performed and analyzed. Vibrational spectra were also calculated. It is also observed that zwitterions of leucine are not stable in gas phase.     

Photoexcitation of dinucleoside radical cations: a time-dependent density functional study

The excited states of dinucleoside phosphates (dGpdG, dApdA, dApdT, TpdA, and dGpdT) in their cationic radical states were studied with time-dependent density functional theory (TD-DFT). The ground-state geometries of all the dinucleoside phosphate cation radicals considered, in their base stacked conformation, were optimized with the B3LYP/6-31G(d) method. Further, to take into account the effect of the aqueous environment surrounding the dinucleoside phosphates, the polarized continuum model (PCM) was considered and the excitation energies were computed by using the TD-B3LYP/6-31G(d) method. From this study, we find that the first transition in all the dinucleoside molecules involves hole transfer from base to base. dG*+pdG and dApdA*+ were found to have substantially lower first transition energies than others with two different DNA bases. Higher energy transitions involve base to sugar as well as base to base hole transfer. The calculated TD-B3LYP/6-31G(d) transition energies are in good agreement with previous calculations with CASSCF/CAS-PT2 level of theory. This TD-DFT work supports the experimental findings that sugar radicals formed upon photoexcitation of G*+ in gamma-irradiated DNA and suggests an explanation for the wavelength dependence found.     

Theoretical and experimental study of the absolute configuration of helical structure of (2R,3S)-Rubiginone A2 analog

A novel analogue of (2R,3S)-Rubiginone A₂ was synthesized as a chiral helical model compound via an eight-step procedure (2.7% overall yield). Quantum methods, such as density functional theory (DFT) at different basis sets of 6-311+(d), 6-311++G(2d,p), were used to compute its optical rotation and electronic circular dichroism at the B3LYP/6-311++G(2d,p) level in the gas phase and in solution using PCM model, respectively. UV corrections were performed in electronic circular dichroism (ECD) simulations to match the experimental ECD well. The suitable computational methods, e.g., B3LYP/6-311++G(2d,p)//B3LYP/6-311++G(2d,p) in the gas phase using zero-point energy in Boltzmann statistics, were found and suggested for optical rotation and circular dichroism computations that can be used for absolute configuration determination of chiral helical compounds.     

The nature and role of 8-deltacyclyl and 7-isodeltacyclyl cations in solvolytic reactions of parent brosylates

Solvolysis of exo-8-deltacyclyl brosylate proceeds directly through a C(2) delocalized cation to exo-8-deltacyclyl acetate. The solvolysis of the endo epimer presents a more complex picture, reacting via a classical deltacyclyl cation, the nonclassical C(2) delocalized cation, and the isodeltacyclyl cation. The solvolysis of exo-7-isodeltacyclyl brosylate generates the 7-isodeltacyclyl ion and subsequently the C(2) delocalized deltacyclyl cation forming 8-deltacyclyl acetate and exo-7-isodeltacyclyl acetate. The cationic intermediates in these three related reaction manifolds are characterized using density functional methods at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) and BPW91/6-311+G(3df, 2p)//BPW91/6-31G(d) levels.     

A computational study of the ground and excited state structure and absorption spectra of free-base N-confused porphine and free-base N-confused tetraphenylporphyrin

Computational investigations into the ground and singlet excited-state structures and the experimental ground-state absorption spectra of N-confused tetraphenylporphyrin tautomers 1e and 1i and N-confused porphines (NCP) 2e and 2i have been performed. Structural data for the ground state, performed at the B3LYP/6-31G(d), B3LYP/6-31+G(d)//B3LYP/6-31G(d), and B3LYP/6-311+G(d)//B3LYP/6-31G(d) levels, are consistent with those performed at lower levels of theory. Calculations of the gas-phase, ground-state absorption spectrum are qualitatively consistent with condensed phase experiments for predicting the relative intensities of the Q(0,0) and Soret bands. Inclusion of implicit solvation in the calculations substantially improves the correlation of the energy of the Soret band with experiment for both tautomers (1e, 435 nm predicted, 442 nm observed in DMAc; 1i, 435 nm predicted, 437 nm observed in CH2Cl2). The x- and y-polarized Q-band transitions were qualitatively reproduced for 1e in both the gas phase and with solvation, although the low-energy absorption band in 1i was predicted at substantially higher energy (646 nm in the gas phase and 655 nm with solvation) than observed experimentally (724 nm in CH2Cl2). Franck-Condon state and equilibrated singlet excited-state geometries were calculated for unsubstituted NCP tautomers 2e and 2i at the TD-B3LYP/SVP and TD-B3LYP/TZVP//TD-B3LYP/SVP levels. Electronic difference density plots were calculated from these geometries, thereby indicating the change of electron density in the singlet excited states. Adiabatic S1 and S2 geometries of these compounds were also calculated at the TD-B3LYP/SVP level, and the results indicate that while 2i is a more stable ground-state molecule by approximately 7.0 kcal mol-1, the energy difference for the S1 excited states is only approximately 1.0 kcal mol-1 and is 6.1 kcal mol-1 for the S2 excited states.     

Comparison of Some Computational Methods for Geometry Optimisation of Phosphorus Acid Derivatives

Several economical methods for geometry optimization, that should be applicable to larger molecules, have been evaluated for 19 phosphorus acid derivatives. MP2/cc-pVDZ geometry optimizations are used as reference points and the geometries obtained from the other methods are evaluated with respect to deviations in bond lengths and angles, from the reference geometries. The geometry optimization methods are also compared to the much used B3LYP/6-31G(d) method. Single point energies obtained by subsequent EDF1/6-31+G(d) or B3LYP/6-31+G(d,p) calculations on the respective equilibrium geometries are also reported relative to the energies obtained from the reference geometries. The geometries from HF/MIDI! optimizations were closer to those of the references than the geometries of the HF/3-21G(d), HF/6-31G(d), and B3LYP/MIDI! optimizations. The EDF1/6-31+G(d) or B3LYP/6-31+G(d,p) single point energies obtained from the HF/3-21G(d), HF/6-31G(d), and B3LYP/MIDI! geometries gave a mean absolute deviation (MAD) from that of the reference geometries of 1.4-3.9 kcal mol m 1 . The HF/MIDI! geometries, however, gave EDF1/6-31+G(d) and B3LYP/6-31+G(d,p) energies with a MAD of only about 0.5 and 0.55 kcal mol m 1 respectively from the energies obtained with the reference geometries. Thus, use of HF/MIDI! for geometry optimization of phosphorus acids is a method that gives geometries of near-MP2 quality, resulting in a fair accuracy of energies in subsequent single point calculations, at a much lower computational cost other methods that give similar accuracies.